The MIANALYZE Procedure

Testing Linear Hypotheses about the Parameters

Linear hypotheses for parameters $\bbeta$ are expressed in matrix form as

$H_0: \mb {L} \bbeta = \mb {c}$

where $\mb {L}$ is a matrix of coefficients for the linear hypotheses and $\mb {c}$ is a vector of constants.

Suppose that $\hat{\mb {Q}_ i}$ and $\hat{\mb {U}_ i}$ are the point and covariance matrix estimates, respectively, for a p-dimensional parameter $\mb {Q}$ from the $i\mr {th}$ imputed data set, i=1, 2, …, m. Then for a given matrix $\mb {L}$ , the point and covariance matrix estimates for the linear functions $\mb {L} \mb {Q}$ in the $i\mr {th}$ imputed data set are, respectively,

$\mb {L} \hat{\mb {Q}_ i}$

$\mb {L} \hat{\mb {U}_ i} \bL ’$

The inferences described in the section Combining Inferences from Imputed Data Sets and the section Multivariate Inferences are applied to these linear estimates for testing the null hypothesis $H_0: \mb {L} \bbeta = \mb {c}$ .

For each TEST statement, the “Test Specification” table displays the $\mb {L}$ matrix and the $\mb {c}$ vector, the “Variance Information” table displays the between-imputation, within-imputation, and total variances for combining complete-data inferences, and the “Parameter Estimates” table displays a combined estimate and standard error for each linear component.

With the WCOV and BCOV options in the TEST statement, the procedure displays the within-imputation and between-imputation covariance matrices, respectively.

With the TCOV option, the procedure displays the total covariance matrix derived under the assumption that the population between-imputation and within-imputation covariance matrices are proportional to each other.

With the MULT option in the TEST statement, the “Multivariate Inference” table displays an F test for the null hypothesis $\mb {L} \bbeta = \mb {c}$ of the linear components.